Is there a way to set depth of field to the _closest_ point on a focus object, or do it via nodes?
You can add a single bone armature object, set it as child of your mesh. Bone lenght 1 meter. Then create an empty in the same location of the tail of the bone and parent it to the bone (Ctrl P - bone). Then set a damped track constraint to the bone, targeting the camera. Then set the empty as focus of the camera DOF.